Details

Time bar (total: 6.6s)

sample81.0ms

Algorithm
intervals
Results
38.0ms108×body2560valid
16.0ms72×body1280valid
7.0ms270×body80nan
6.0ms40×body640valid
2.0ms14×body320valid
1.0ms10×body160valid
1.0ms12×body80valid

simplify94.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0197
1427
2777
31467
42427
54177
627897
750017

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.6b

localize8.0ms

Local error

Found 4 expressions with local error:

0.0b
(- 1.0 (* 5.0 (* v v)))
0.0b
(/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))
0.1b
(* 5.0 (* v v))
0.6b
(acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))

rewrite19.0ms

Algorithm
rewrite-expression-head
Rules
19×add-sqr-sqrt
14×add-cube-cbrt *-un-lft-identity
12×times-frac
11×add-exp-log add-cbrt-cube
9×pow1
6×add-log-exp
4×associate-/r* difference-of-squares
3×flip3-- associate-*l* pow-prod-down prod-exp flip-- cbrt-unprod associate-/l*
2×associate-/r/ associate-/l/
1×cbrt-undiv acos-asin sub-neg frac-2neg diff-log div-sub div-exp associate-*r* clear-num *-commutative div-inv unswap-sqr
Counts
4 → 75
Calls
4 calls:
3.0ms
(- 1.0 (* 5.0 (* v v)))
8.0ms
(/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))
6.0ms
(* 5.0 (* v v))
1.0ms
(acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))

series172.0ms

Counts
4 → 12
Calls
4 calls:
61.0ms
(- 1.0 (* 5.0 (* v v)))
83.0ms
(/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))
24.0ms
(* 5.0 (* v v))
4.0ms
(acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))

simplify40.0ms

Algorithm
egg-herbie
Counts
87 → 87
Iterations

Useful iterations: 2 (32.0ms)

IterNodesCost
0355664
11356609
25001605

prune198.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.6b

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))
0.0b
(- (/ PI 2) (asin (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))))
0.1b
(* 5.0 (* v v))
0.7b
(asin (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))

rewrite28.0ms

Algorithm
rewrite-expression-head
Rules
24×add-sqr-sqrt
16×*-un-lft-identity
14×add-cube-cbrt
13×times-frac
11×add-exp-log add-cbrt-cube
9×pow1
6×add-log-exp difference-of-squares
4×associate-/r*
3×flip3-- associate-*l* pow-prod-down prod-exp flip-- cbrt-unprod associate-/l*
2×asin-acos associate-/r/ associate-/l/
1×cbrt-undiv sub-neg frac-2neg diff-log div-sub div-exp associate-*r* clear-num *-commutative div-inv distribute-lft-out-- associate--r- unswap-sqr
Counts
4 → 79
Calls
4 calls:
12.0ms
(/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))
7.0ms
(- (/ PI 2) (asin (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))))
6.0ms
(* 5.0 (* v v))
1.0ms
(asin (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))

series143.0ms

Counts
4 → 12
Calls
4 calls:
84.0ms
(/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))
30.0ms
(- (/ PI 2) (asin (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))))
25.0ms
(* 5.0 (* v v))
3.0ms
(asin (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))

simplify43.0ms

Algorithm
egg-herbie
Counts
91 → 91
Iterations

Useful iterations: 2 (34.0ms)

IterNodesCost
0409840
11459784
25001780

prune238.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.6b

localize20.0ms

Local error

Found 4 expressions with local error:

1.0b
(/ (- (pow (/ PI 2) 3) (pow (asin (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))) 3)) (+ (* (asin (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))) (+ (asin (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))) (/ PI 2))) (* (/ PI 2) (/ PI 2))))
1.0b
(pow (asin (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))) 3)
1.0b
(pow (/ PI 2) 3)
1.8b
(+ (asin (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))) (/ PI 2))

rewrite70.0ms

Algorithm
rewrite-expression-head
Rules
244×add-sqr-sqrt
149×times-frac
102×*-un-lft-identity
96×difference-of-squares
88×unpow-prod-down cube-prod
60×add-cube-cbrt
42×sqr-pow
33×associate-/l*
20×distribute-lft-out--
10×add-exp-log add-cbrt-cube
8×associate-*r/ associate-/r/
6×pow1 pow-unpow frac-add add-log-exp
5×flip3-+ flip-+
4×difference-cubes
3×pow-exp associate-/r* div-inv rem-cube-cbrt
2×cbrt-undiv cube-mult frac-times pow-to-exp pow-pow unpow3 div-exp associate-*l/ associate-/l/
1×+-commutative cube-div associate-+l- asin-acos flip3-- frac-2neg div-sub clear-num sum-log flip-- distribute-lft-out
Counts
4 → 240
Calls
4 calls:
43.0ms
(/ (- (pow (/ PI 2) 3) (pow (asin (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))) 3)) (+ (* (asin (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))) (+ (asin (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))) (/ PI 2))) (* (/ PI 2) (/ PI 2))))
3.0ms
(pow (asin (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))) 3)
5.0ms
(pow (/ PI 2) 3)
6.0ms
(+ (asin (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))) (/ PI 2))

series510.0ms

Counts
4 → 10
Calls
4 calls:
433.0ms
(/ (- (pow (/ PI 2) 3) (pow (asin (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))) 3)) (+ (* (asin (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))) (+ (asin (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))) (/ PI 2))) (* (/ PI 2) (/ PI 2))))
50.0ms
(pow (asin (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))) 3)
0.0ms
(pow (/ PI 2) 3)
26.0ms
(+ (asin (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))) (/ PI 2))

simplify222.0ms

Algorithm
egg-herbie
Counts
250 → 250
Iterations

Useful iterations: 1 (24.0ms)

IterNodesCost
094410059
146339809
250019809

prune676.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.6b

localize28.0ms

Local error

Found 4 expressions with local error:

1.0b
(/ (- (pow (/ PI 2) 3) (pow (asin (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))) 3)) (+ (* (asin (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))) (+ (asin (/ (- 1.0 (* 5.0 (pow v 2))) (- (pow v 2) 1.0))) (* 1/2 PI))) (* (/ PI 2) (/ PI 2))))
1.0b
(pow (asin (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))) 3)
1.0b
(pow (/ PI 2) 3)
1.8b
(+ (asin (/ (- 1.0 (* 5.0 (pow v 2))) (- (pow v 2) 1.0))) (* 1/2 PI))

rewrite63.0ms

Algorithm
rewrite-expression-head
Rules
244×add-sqr-sqrt
149×times-frac
100×*-un-lft-identity
96×difference-of-squares
88×unpow-prod-down cube-prod
60×add-cube-cbrt
42×sqr-pow
33×associate-/l*
20×distribute-lft-out--
10×add-exp-log add-cbrt-cube
8×associate-*r/ associate-/r/
6×pow1 pow-unpow frac-add add-log-exp
5×flip3-+ flip-+
4×difference-cubes
3×pow-exp associate-/r* div-inv rem-cube-cbrt
2×cbrt-undiv cube-mult frac-times pow-to-exp pow-pow unpow3 div-exp associate-*l/ associate-/l/
1×+-commutative cube-div associate-+l- asin-acos flip3-- frac-2neg div-sub clear-num sum-log flip--
Counts
4 → 239
Calls
4 calls:
39.0ms
(/ (- (pow (/ PI 2) 3) (pow (asin (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))) 3)) (+ (* (asin (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))) (+ (asin (/ (- 1.0 (* 5.0 (pow v 2))) (- (pow v 2) 1.0))) (* 1/2 PI))) (* (/ PI 2) (/ PI 2))))
3.0ms
(pow (asin (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))) 3)
5.0ms
(pow (/ PI 2) 3)
4.0ms
(+ (asin (/ (- 1.0 (* 5.0 (pow v 2))) (- (pow v 2) 1.0))) (* 1/2 PI))

series507.0ms

Counts
4 → 10
Calls
4 calls:
431.0ms
(/ (- (pow (/ PI 2) 3) (pow (asin (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))) 3)) (+ (* (asin (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))) (+ (asin (/ (- 1.0 (* 5.0 (pow v 2))) (- (pow v 2) 1.0))) (* 1/2 PI))) (* (/ PI 2) (/ PI 2))))
50.0ms
(pow (asin (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))) 3)
0.0ms
(pow (/ PI 2) 3)
27.0ms
(+ (asin (/ (- 1.0 (* 5.0 (pow v 2))) (- (pow v 2) 1.0))) (* 1/2 PI))

simplify218.0ms

Algorithm
egg-herbie
Counts
249 → 249
Iterations

Useful iterations: 2 (131.0ms)

IterNodesCost
097110012
144789755
250019607

prune739.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.6b

regimes178.0ms

Accuracy

0% (0.0b remaining)

Error of 0.6b against oracle of 0.5b and baseline of 0.6b

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03533
13533

end0.0ms

sample2.3s

Algorithm
intervals
Results
987.0ms2978×body2560valid
556.0ms2475×body1280valid
222.0ms8063×body80nan
199.0ms1259×body640valid
76.0ms647×body320valid
33.0ms408×body160valid
11.0ms233×body80valid